Question

A 5.0-cm tall light bulb is placed a distance of 50 cm from a convex mirror having a focal length of 10 cm. What is the image height?

• A. $\frac{6}{5}cm$
• B. $\frac{-6}{5}cm$
• C. $\frac{-5}{6}cm$
• D. $\frac{5}{6}cm$

Answer 1

Answer: (D)

$\frac{5}{6}cm$

Using mirror formula,
$\frac{1}{u}$ + $\frac{1}{v}$ = $\frac{1}{f}$
$\frac{1}{-50}$ + $\frac{1}{v}$ = $\frac{1}{10}$
(u is negative and f is positive for a convex mirror)
Solving, we get:
$v=\frac{50}{6}cm$

Using the formula for magnification,
$m=-\frac{v}{u}$ = $\frac{h^{\prime }}{h}$
$-\frac{50/6}{-50}=\frac{h^{\prime }}{5}$
$h^{\prime }=\frac{5}{6}cm$